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Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

机译：操作员推理，用于非多项式非线性术语的系统的非侵入式模型减少

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摘要

This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations. (C) 2020 Elsevier B.V. All rights reserved.
机译：该工作提出了非侵入式模型还原方法，以学习具有在空间局部的非多项式非线性术语的动态系统的低维模型，并且以分析形式给出。与侵扰性的最先进的模型减少方法形成对比，因此需要全面了解控制方程和离散动态系统的完整模型的运营商，所提出的方法只需要分析中的非多项式术语从使用潜在的黑匣子全模型求解器计算的快照，从表格上表格并了解其余动态。所提出的方法通过最小二乘问题学习线性和多项式非线性动力学的操作员，其中给定的非多项式术语在右侧结合在一起。最小二乘问题是线性的，因此可以在实践中有效地解决。所提出的方法是关于部分微分方程治理的三个问题，即扩散反应Chafee-Infante模型，反应性流动的管状反应器模型以及描述化学分离过程的分批色谱模型。数值结果提供了证据表明，所提出的方法了解降低模型，以实现可比准确性的模型，作为采用最先进的侵入式模型减少方法，需要完全了解控制方程式的模型。 （c）2020 Elsevier B.v.保留所有权利。

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